The interaction between the two main Th cell subsets, Th1 and Th2, is complex and occurs at several different levels. The differentiation of Th1 or Th2 cells from a single naive precursor has been shown to be dependent on many factors, including the cytokine milieu created by the invading pathogen and factors such as the dose of antigenic peptide and the type of costimulatory molecules present at the time of response initiation. We have been using mathematical modeling to study these complex interactions, both at the level of crossregulation and differentiation, using in vitro systems with well-defined cell populations and conditions, and have been able to identify certain critical parameters. The next stage of these studies is to use the mathematical and experimental tools that we have developed to understand the immune response in vivo. We have now developed a new mathematical model which allows the analysis of the development of Th1 and/or Th2 responses in vivo and which can reproduce many of the experimental findings that we have recently obtained. The work over the next five years will involve the detailed analysis of this model and the validation of the results obtained using novel in vivo experimental strategies. The specific aims of the proposal are: 1) To study in vivo Th1/Th2 differentiation and crossregulation using a mathematical model; 2) To estimate the values of the parameter appearing in the model by studying the in vivo immune response to specific peptides following the transfer of TCR transgenic T cells; 3) To study the Th1/Th2 balance in an experimental model of tumor rejection using both experimental and mathematical approaches; 4) To develop a new mathematical language that better captures the reality of the immune response. Overall these studies will continue our work as a unique collaboration between immunologists and mathematicians and will move into the new arena of in vivo immune responses, and the factors that determine Th1/Th2 dominance in vivo, which is the area to which mathematics may have the most to contribute.